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Unformatted text preview: oss-section,
but it works for any cross-section. Hence the ﬂow rate vAθ cos θ = vA. Even though
the area Aθ is larger than A (by a factor of cos θ), the height/width of the slanted Page 1 of 3 Math 1920 Workshop 1: Work and Flux Solutions column is smaller than v by the same factor. Hence the volumes and ﬂow rates, in
part a and b are the same.
One can also imagine a deck of cards, with cards laid horizontally along the arrows
shown in the ﬁgure. Deck in ﬁgure (b) is a displaced version of the deck in ﬁgure (a),
and hence has the same volume.
c) In part a, the velocity ﬁeld is v = vˆ and the area vector S = Aˆ. The ﬂux is v · S = vA....
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